Publication
Lyapunov-Based Certified Region-of-Attraction Estimation for Constrained LQR-Controlled Systems
Ece Nur Demirhan Coskun; Kemal Caglar Coskun; Christoph Lüth; Dieter Hutter
In: 19th IEEE Dallas Circuits and Systems Conference. IEEE Dallas Circuits and Systems Conference (DCAS-2026), 19th IEEE Dallas Circuits and Systems Conference (DCAS), April 10-12, Dallas, Texas, USA, IEEE, 2026.
Abstract
Many cyber-physical systems operate in safety-critical settings where formal stability guarantees are required. In this context, methods for Region-of-Attraction (ROA) are of particular interest, as they provide certified characterizations of the initial states from which system executions remain stable despite disturbances and constraints.
We present a Lyapunov-based method for computing certified ROAs for constrained nonlinear systems controlled by Linear Quadratic Regulators (LQRs). The approach constructs a composite Lyapunov function that combines a problem-informed energylike term with the LQR cost-to-go, and leverages a targeted sampling strategy to efficiently identify invariant sublevel sets while preserving formal guarantees. Rather than proposing a universal ROA solver, this work presents a practical and sound framework that can be instantiated in a system-specific manner. The approach is evaluated on a torque-limited inverted pendulum benchmark and produces certified ROAs that are less conservative than those obtained using standard quadratic Lyapunov functions and analytic baselines.